Is accuracy more important than precision in near‐surface refraction seismology?

Abstract

ABSTRACTThe ubiquity of non‐uniqueness in near‐surface refraction seismology emphasises the importance of making a clear distinction between accuracy, that is, the validity of the model, and precision, that is, traveltime misfit errors. Non‐uniqueness can be resolved by identifying the most probable model within a global model space, based on the generalised reciprocal method (GRM), containing all geologically reasonable seismic velocities. All models within this model space have comparable misfit errors.The strategy involves three elements. First, the XY parameter of the GRM facilitates a more effective differentiation of the various models of the seismic velocities in both the weathered and sub‐weathered regions than is possible with simplistic comparisons of traveltime misfit errors. Second, all valid models of the seismic velocities in the weathered and sub‐weathered regions are restricted to those which employ the same XY value in both regions. Finally, the most probable model employs the optimum XY value, which is that XY value(s) which results in the simplest model of the GRM‐derived seismic velocities in the sub‐weathered region.Under suitable conditions where the refracting interface is sufficiently irregular, the optimum XY value can be measured to a precision of plus/minus half the station spacing. However, where that is either not possible or not undertaken, then a uniform velocity equivalent value can be computed from the cross‐over distance, with an inferred precision of plus/minus the optimum XY value.The significance of non‐uniqueness in any investigation can be demonstrated with two models. The first employs the uniform velocity model equivalent of the optimum XY value, whereas the second employs an XY value equal to the cross‐over distance. These two models represent the end members of the set of models which are consistent with the traveltime data. They span the range of seismic velocities in the weathered layers from uniform or constant values to the hyperbolic cosine function. The latter represents the maximum vertical velocity gradient which is consistent with linear traveltime graphs and which approximates the vertical velocity gradients commonly used in many implementations of automatic refraction tomography.Irrespective of whether the optimum XY value is determined with a precision of plus/minus half the station spacing or plus/minus the optimum XY value, the optimum XY value for uniform layers is commonly one quarter of the cross‐over distance. Therefore, the optimum XY value provides a more precise measure of the accuracy of the seismic velocities than is possible with traveltime misfit errors.